Semi-analytical valuation of an option on the maximum of two assets under a stochastic volatility model with stochastic long-term mean and stochastic liquidity

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Abstract

This paper proposes a semi-analytical valuation framework for a European call option on the maximum of two assets under a two-factor stochastic volatility model that incorporates both stochastic long-term means and stochastic liquidity risk. By applying the Feynman–Kac theorem, the joint characteristic function of the two liquidity-adjusted log-prices is explicitly derived. Using this joint characteristic function, a semi-analytical pricing formula for the option is obtained through measure changes and bivariate Fourier inversion techniques. The formula is validated against Monte Carlo simulation, and comparisons with nested benchmark models quantify the incremental pricing effects of stochastic liquidity and the stochastic long-term mean. Finally, through various numerical examples, a sensitivity analysis is conducted to illustrate how changes in significant parameters affect the option’s price.

Keywords

option on the maximum / stochastic volatility / stochastic liquidity risk / stochastic long-term mean

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